Numerical solution of a two-dimensional parabolic transmission problem
Bosko Jovanovic 1, Lubin G. Vulkov 21 University of Belgrade, Faculty of Mathematics, 11000 Belgrade, Serbia.
2 University of Rousse, Department of Mathematics, 7017 Rousse, Bulgaria.
Received by the editors May 13, 2009.
An initial boundary value problem for a two-dimensional parabolic equation in two disconnected rectangles is investigated. A finite difference scheme approximating this problem is proposed and analyzed. An estimate of the convergence rate, compatible with the smoothness of the input data (up to a logarithmic factor of the mesh-size), is obtained.
AMS subject classifications: 65M15
Key words: Transmission problem, initial-boundary value problem, disconnected domains, Sobolev spaces, finite differences, convergence rate.
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